a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% per year. what will the…

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (purchase price), $r$ is the annual depreciation rate (in decimal), and $t$ is the number of years.

Step2: Convert the rate to decimal

The depreciation rate is $11.75%$, so in decimal form, $r = \frac{11.75}{100} = 0.1175$.

Step3: Substitute the values into the formula

We have $P = 17600$, $r = 0.1175$, and $t = 11$. Plugging these into the formula: $V = 17600(1 - 0.1175)^{11}$.

Step4: Calculate the value inside the parentheses

First, calculate $1 - 0.1175 = 0.8825$.

Step5: Calculate the exponentiation

Now, calculate $0.8825^{11}$. Using a calculator, $0.8825^{11} \approx 0.2744$.

Step6: Multiply by the initial price

Multiply this result by the initial price: $V = 17600 \times 0.2744 \approx 4829.44$.

Answer:

The value of the car after 11 years will be approximately $$4829.44$.